Gatorbait

OORR ??

Are you Are you a a

Two rivalries in one Two rivalries in one table!table!!

Garnet and Gold or Orange and Blue? You decide!

Garnet Garnet and Goldand Gold

Orange Orange and Blueand Blue

TotalTotal

Males 66 44 1010

Females 1010 33 1313

Total 1616 77 2323

• How many males like orange and blue?

• What does the number 16 represent?

• How many people were surveyed?• How would you determine if there

was a possible association between favorite team colors and gender?

A survey was conducted and the results are shown in the table below. Try to answer the following questions.

Two-Way Frequency Tables

Florida Standard

MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in data.

Objectives

• Create and interpret a two-way frequency table from two categorical variables.

• Read and interpret data displayed in a two-way table and calculate the relative frequencies.

• Describe patterns and trends observed in the data.

What is a two-way frequency table?

TOTAL88 1313 2121

1111 2121 3232

TOTAL 1919 3434 5353

LOOKS LIKE

LOOKS LIKE

CATE

GO

RY B

CATEGORY A Two-Way Table

A table used to study the relationship between two categorical variables.

Joint and Marginal Frequency

TOTAL

TOTAL

CATEGORY A

CATE

GO

RY B

88 1313

1111 2121 32

535334341919

21

Joint Joint FrequencFrequenc

yyThe values that make up the BODY of the table.

Marginal Frequenc

yThe ROW and COLUMN totals for each category.

25 seniors were surveyed and asked which college football team they liked best. Out of the 17 that liked Florida State, 6 were females. There was a total of 13 females surveyed. Summarize the data in a two-way table.

Florida State

Florida Total

Males

Females

Total

Ex. 1 Construct a Two-Way Table

Fill in the values you already know. Determine if each value

represents a JOINT or MARGINAL frequency.

Recall that JOINT frequency goes in the body (yellow area) of the table, and MARGINAL frequency goes in the row and column total (green area) of the table.

Use reasoning to find the remaining values.

TIPS FOR COMPLETING THE

TABLE

Guided Practice

Construct a Two-Way TableThere were 45 students in gym class that were asked if they like football or basketball and if they liked Nike or Adidas. Out of the 19 students that liked basketball, 7 liked Adidas. There were 23 students that liked Adidas. Use reasoning to find the missing values.

Nike Adidas Total

Football

Basketball

Total

Calculate Row Relative Frequencies

Relative frequency is the ratio of the subtotal to the total

Florida State

Florida

Total

Males 11 1 12

Females 6 7 13

Total 17 8 25

For each row, find the ratio of each joint frequency to the marginal frequency for that row.

Florida State

Florida Total

Males

Females

Total

The relative frequencies in the body of the table are called conditional relative frequencies.

Calculate Column Relative Frequencies

Relative frequency is the ratio of the subtotal to the total

Florida State

Florida

Total

Males 11 1 12

Females 6 7 13

Total 17 8 25

For each column, find the ratio of each joint frequency to the marginal frequency for that column.

Florida State

Florida Total

Males

Females

Total

Guided PracticeCalculate Relative Frequencies

Calculate the missing row relative frequencies for the table.

Round to the nearest hundredth. Show all work.

Calculate the missing column relative frequencies for the table.

Association between two categorical variables occur when the conditional relative frequencies for the rows or columns differ significantly.

There is little to no association between two categorical variables when the conditional relative frequencies for the rows or columns are equal or evenly distributed.

Read, Interpret, and Draw Conclusions

Two-WayFrequency

Florida State

Florida

Total

Males 11 1 12

Females 6 7 13

Total 17 8 25

Which table can we use to determine the percentage of males that like Florida? What is the percentage?

Which table can we use to determine the percentage of females that took the survey? What is the percentage?

[ROW]Relative

FrequenciesFlorida State

Florida

Total

Males 0.92 0.08 1.00

Females 0.46 0.54 1.00

Total 0.68 0.32 1.00

[COLUMN]Relative

FrequenciesFlorida State

Florida

Total

Males 0.65 0.13 0.48

Females 0.35 0.88 0.52

Total 1.00 1.00 1.00

Use the tables to answer the following questions.

Based on the row conditional frequencies, is there evidence of an association between gender and favorite college football team?

What do the numbers 7, 11, and 12 represent? Are they JOINT or MARGINAL frequencies?

Guided Practice

Read, Interpret, and Draw Conclusions Refer back to the tables in problem 1 & 2 to answer the following questions.

1. What is the joint frequency of students who like Nike?

2. What is the marginal frequency of students who like basketball?

3. Of the students who like Nike, what percentage like football as well?4. What percentage of the students like basketball and Adidas?

5. Is there evidence of an association between the sport a student likes and the brand of sneakers they like? Explain.

What have you learned?

Refer back to the opening problem. Answer the questions again. How do your “post lesson” answers compare to your “pre-lesson” answers? Are they the same or different?

• How many males like orange and blue?

• What does the number 16 represent?

• How many people were surveyed?

• How would you determine if there was a possible association between favorite team colors and gender?

A survey was conducted and the results are shown in the table below. Answer the following questions.

Garnet Garnet and Goldand Gold

Orange Orange and Blueand Blue TotalTotal

Males 6 4 10

Females 10 3 13

Total 16 7 23